Lecture Notes: Interpreting Scatter Plots

Introduction to Scatter Plots

• A scatter plot is a graph used to display values for typically two variables for a set of data.
• Points on the scatter plot represent individual data points.

Types of Associations in Scatter Plots

No Association

• Definition: No discernible pattern between the x-axis and y-axis values.
  • Example: Height vs. Maths marks; no correlation between a person's height and their maths ability.

Positive Association

• Definition: As values on the x-axis increase, values on the y-axis also increase.
  • Example: Temperature vs. Ice cream sales; higher temperatures lead to increased ice cream sales.

Negative Association

• Definition: As values on the x-axis increase, values on the y-axis decrease.
  • Example: Temperature vs. Soup sales; higher temperatures lead to decreased soup sales.

Other Associations

• Patterns may vary depending on different factors like time of day.

Linear vs. Nonlinear Associations

Linear Association

• Definition: A pattern that can be represented by a straight line.

Nonlinear Association

• Definition: A pattern best represented by a curve or another shape.
  • Example: Exponential growth seen in COVID-19 graphs.

Strength of Associations

Strong Association

• Data points are close together, showing a clear pattern.

Moderate Association

• Data points are more spread out but still show a perceptible pattern.

Weak Association

• Data points are scattered with less obvious pattern direction.

Outliers in Scatter Plots

• Definition: Data points that deviate significantly from the overall pattern.
• Example: Students who do much homework but have low maths marks, or vice versa.

Practical Interpretation

• Use mathematical terminology (e.g., moderate positive association, outliers) to describe and interpret scatter plots.
• Interpretation includes assessing the relationship, determining strength, and identifying outliers.

Conclusion

• With understanding of these concepts, one can look at a scatter plot and interpret the relationships, including identifying any outliers.